Solveeit Logo

Question

Physics Question on laws of motion

A truck is moving on a friction less surface with uniform velocity of 10m/s10 \,m/s . A leak occurs in the water tank of the truck at the rate of 2kg/s2\, kg/s . What is the speed of truck after 50s50 \,s if the mass of truck is 100kg100\, kg and mass of water in the truck initially was 100kg100 \,kg ?

A

20m/s20 \, m/s

B

10m/s10 \, m/s

C

5m/s5 \, m/s

D

None of these

Answer

None of these

Explanation

Solution

Given that, u=10m/su = 10 m/ s, dmdt=2kg/s\frac{dm}{dt}=2 \, kg/s
Total mass of the truck,
M=(100+100)kg=200kgM = \left(100 + 100\right) kg = 200\, kg
We know that,
F=udmdtF=\frac{u\,dm}{dt}
or F=10×2=20NF=10\times2=20\,N
or Ma=20NMa = 20 \,N
or 200a=20N200a = 20 \,N
or a=20200m/s2a=\frac{20}{200} m/ s^{2}
=110m/s2=\frac{1}{10} m / s^{2}
Now, we know that,
a=vuta=\frac{v-u}{t} [u=10m/s,t=50s]\left[u=10 m/ s, t=50\,s\right]
110=v1050\Rightarrow \frac{1}{10}=\frac{v-10}{50}
v=15m/s\Rightarrow v=15 m/ s